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Polarized Armies

Defending troops are all partially polarized in their defense. Ranged troops are twice as good at fighting ranged enemies than they are at fighting melee troops, and melee defenders are twice as good against melee attackers than at ranged.
Attackers however, are completely polarized. A ranged attacker ONLY has ranged attack, with no melee attack. The same is true for melee attackers.
For this reason in a normal battle situation, with no bonuses and with (for example) 100 ranged attackers, 100 melee attackers, 100 ranged defenders and 100 melee defenders the defenders will win. This is because each of the ranged attackers will give 1 RA (ranged attack) and each of the melee attackers will give 1 MA (melee attack), but ranged defenders will give 1 RD(ranged defense) in addition to 0.5 MD (melee defense) and melee defenders will give 1 MD in addition to 0.5 RD. Therefore, this battle would work out to be 100RA+100MA vs 150RD+150MD. A clear victory for the defender.
If, however, the attacker sent a polarized army, for instance, 200 ranged attackers instead of the 100 melee attackers, the same battle would have been won by the attacker. The is because while the ranged defenders would still have 1RD, they would no longer give the 0.5MD, and while the melee defenders still have the 0.5RD, they would loose the 1MD. The attacker would be denying their enemy defense. Therefore, this battle would turn into 200RA vs 150RD. A clear victory for the attacker.
I would therefore argue, that polarized armies are better than mixed armies.
Arguments against polarized armies:
1.But the defender will be able to (in the case of a ranged polarized army) move all his ranged troops on the walls!
This is true, but not as effective as people imagine. Firstly, most players will not have only ranged defenders, as this leaves them open to attack from polarized melee armies. This means that the total ranged defense of the defender is still the same, even if he shifts his ranged defenders on the walls. In addition, the same principle of denying the defender his defense applies. Lets say that we are attacking 200 ranged defenders with 200 ranged attackers. The attackers will again have 200RA vs 200RD, resulting in a tie. If we replaced 100 ranged attackers with 100 melee attackers, making it a mixed army, we would now have 100MA and 100RA vs 100MD and 200RD. Meaning a victory for the defender. The point of polarized armies is to deny the enemy their melee defense, and this can also be done against ranged defenders.
2.But such a method would still not work against the combination of lime bombs and veteran swordsmen!
This is true, but it is also true that a polarized ranged army would work better than a mixed armies. 200 veteran swordsmen with lime bombs can be approximated to have about 500MD (2.5 per soldier) and 300RD (1.5 per soldier). If one sent a mixed army, this would result in a total defense of 800, however, sending a polarized ranged army would deny the defender his 500MD, and so weakening the defense simply by never engaging it, resulting in a defense of 300RD. (it should also be noted that vet swordsmen have lower defense per food consumption than other troops.)
3. But could not the alliance 'e the defender support the defender with really many ranged defenders?
This is true, but not helpful to discussion. The fact is that ANY attack can easily be negated if we assume that the alliance of the defender is capable of magically conjuring 10,000 defenders out of thin air. The point is to make the enemy loose more troops than you do, or in other words to gain a high kill/death ratio.
Admissions:
I am fully aware, that I have massively simplified the situations. Defenders are usually slightly stronger than attacks, there are different types of defenders and attacks, and I ignored the different wall sections or courtyard bonuses. In the end, battles are usually won by tools and commander bonuses, not troop selection. However, I feel that this is a somewhat significant factor in determining the winner of a battle.
Anyway, can any of you find other arguments for or against this theory? Can you find flaws in my reasoning? Please, share your thoughts and opinions, so that any mistakes I may have made can be corrected.

Two years of Playing GGE: Independent Alliance and None Ruby Players
How GGS handles our Feedback
Why I decided to Leave
Thoughts on the Legendary Update
Achieved title of "the terrible", on the 8th of August 2014, without buying rubies, and while playing in an independent alliance.
Comments
By not clicking these you support killing innocent dragons. So don't be mean and click them
What's your favorite apple device?
Second, assume you ONLY has a full M Def. and you got attack by a full M Att. then the M Def. will use his full MD (because he can fully concentrate to use his MD). The same case, but you got attack by a full R Att. then the M Def. will use his full RD. Now 3rd scenario, you got attack by a mixed M and R Att., it doesn't make sense if the M Def. then use BOTH full his RD and MD (because he has to split his concentration to BOTH M & R). It got to be a fraction of his RD and his MD, in such that these fraction is most likely depends on the MA/RA ratio and logically should sum to 1.
How these fraction factors are calculated is a well guarded secret via FIPS 140-2 Level 4 process ^^ and pledged to be defended by GGS developer till their last paycheck, unless we are a mathematician that has access to tons of complete battle reports, I believe it will be futile trying to figure it out.
Not to mention once we got total MA/RA and MD/RD power, there is another super duper secret formula (no, it's not 1+1=2) to figure out the loss on each side.
And anyway one wise man told me (starts with B and he loves Turnip), there is actually no point to trying to figure the EXACT formula, as GGS just change everything again (intentionally or via super bugs) after a few months anyway. I believe many have tried and failed.
What important is to understand the basic mechanic of it and don't think about it too much, it's just a game dude....
Well, I would say that what we do know about the formulas used to calculate losses, victories and casualties is that they use the total defense as a factor. This is a guess, but it would also be the most logical thing to do on the part of GGE. Therefore, if we deny the enemy part of his defense by not giving him a target to allocate it to, we know that the total defense would be less, and I would consider it very odd if, in the calculations of GGE, a smaller defense where as or more powerful than a bigger one.
Two years of Playing GGE: Independent Alliance and None Ruby Players
How GGS handles our Feedback
Why I decided to Leave
Thoughts on the Legendary Update
Achieved title of "the terrible", on the 8th of August 2014, without buying rubies, and while playing in an independent alliance.
Its nice to have a debate on this
I think its somewhat this-
A veteran spearman has x Health Points.
It has y melee defense points
It has z ranged defense points.
Now, think like this that a vet spearman has good melee shield
But he is highly exposed to ranged weapons. Or his armour against ranged weapons is low.
So, A vet maceman would take 90% from x Health Points
He fights 100% y ( melee defense power)
But it weakens him overall & reduces his z ( ranged defense power)
So now, a crossbowman comes with a attack power
normally, his rang attack power is less that vet spearman's rang def.
But he is weakened.
So the vet spear gets killed.
But now again, crossbowman is injured.
Here is how it somewhat works.
I have stopped trying to figure out or predict exactly what my losses will be. All I need is a ball park, if my total M Att. Pwr. is 130% higher then the total M Def. Pwr while my total R Att. Pwr is 180% higher then the total R Def. Pwr, then I know I will take higher casualty on my poor M Attackers. And so far it has been working nicely for me